All Questions
Tagged with applications optimization
44
questions
6
votes
1
answer
86
views
Minimize travel time of a group of people with a motorbike
Problem: A group of $n$ people ($n\geq2$) want to travel from A to B but they can only either walk or use a motorbike (fit 2 people) [note that there is exactly $1$ motorbike for them to use]. Given ...
2
votes
1
answer
113
views
Standard definition of a game in game theory
Sorry for my naive question, but at the moment I can't quite figure it out.
I'm consulting various documents on game theory in order to get the standard definition of what a game (and an associated ...
- 21
10
votes
2
answers
345
views
Applications of Linear Programming to pure mathematics
This semester I'm taking a course in Linear Programming. While the topic is very interesting, all the applications I can find about this topic seem to be outside of mathematics. What are some ...
- 457
2
votes
0
answers
121
views
Examples of a gradient flow
Suppose we have a gradient flow in $\mathbb{R}^n$ :
$$\frac{d}{dt}x(t)=-\nabla F(x(t)), \qquad x(0)=x_0.$$
where $F : \mathbb{R}^n \to \mathbb{R}$ and $x : \mathbb{R}_+ \to \mathbb{R}^n$. What are ...
- 41
1
vote
0
answers
25
views
Strategies to find the best basis function on a Hilbert space
Consider the Hilbert space associated with the $L^p$-norm. I'm interested to find the best (in the sense of the most sparse) truncated approximation for isomorphic functions in this space. Naturally, ...
- 165
2
votes
1
answer
46
views
Applications of SGD outside learning tasks
Are there applications, outside of machine learning, where stochastic gradient descent (SGD) is the preferred method of optimization?
By SGD, I mean any first-order method which approximates the true ...
- 299
3
votes
2
answers
126
views
How are the functions determined for real-world applications (business, population models, etc.) of calculus?
The following problem has been taken from Paul's Online Notes:
"We need to enclose a rectangular field with a fence. We have 500 feet of fencing material and a building is on one side of the ...
- 33
3
votes
1
answer
284
views
Estimation of $\lambda$, $\mu$, and $\sigma^2$ given observations of $Z=X+Y$, $X\sim\text{Poi}(\lambda)$, $Y\sim\mathcal N(\mu,\sigma^2)$
Let $X\sim\operatorname{Poisson}(\lambda)$ and $Y\sim\mathcal N(\mu,\sigma^2)$ be independent and define $Z=X+Y$. The density of $Z$ can be described as an infinite Gaussian mixture of the form
$$
f_Z(...
- 6,127
0
votes
0
answers
49
views
Application of differentiation based on electricity consumption
A utility company has a small power plant that can produce a kilowatt hours of electricity daily at a cost of 10 - (𝑥/10^5) cents each for 0 < x < 8 x 10^5. Consumers will use 10^5(10 - p/2) ...
- 9
10
votes
1
answer
487
views
Nontrivial applications of tropical mathematics to optimization (soft question)
I have been looking into tropical algebra/geometry for a research problem I'm working on in optimization. Tropical math gets referenced a lot in the literature, but it seems to me that its mostly just ...
- 395
1
vote
0
answers
35
views
Is it possible to get no solution from an optimal stopping problem
I recently read about the 37-percent rule as the solution to the secretary problem.
It says
To have the highest chance of getting the best applicant from a pool of applicants, you should interview ...
- 11
2
votes
2
answers
884
views
How should I learn from proofs in Applied Mathematics?
I am aware that similar questions have been asked here and elsewhere about how to learn from proofs. Some common advice is:
Most proofs are written in a polished form, not how they were first ...
- 492
1
vote
0
answers
31
views
"Gaps in the Mats" problem
Problem Background*
The mat at your karate dojo composed of 160 square interlocking foam tiles. Along each edge of each tile, there are has five "teeth" (10cm long) and five spaces-for-teeth (again ...
- 111
16
votes
1
answer
5k
views
What are the use cases of the Dirichlet energy in computer vision?
I am reading a paper, in the context of computer vision, that mentions the "famous" Dirichlet energy. I am not familiar with this Dirichlet energy, but apparently we can minimise it. What ...
user168764
2
votes
0
answers
323
views
Practical applications of semidefinite programming
I am looking for practical applications of semidefinite- programming. So far, I found that the low-rank matrix completion problem (recomendendattion matrices) can be expressed as a semidefinite ...
- 21